Question

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0${}^{\circ }$C and 90${}^{\circ }$C respectively. The temperature of junction of the three rods will be

• A. 45${}^{\circ }C$
• B. 60${}^{\circ }C$
• C. 30${}^{\circ }C$
• D. 20${}^{\circ }C$

Answer 1

Answer: (B)

Let $\theta$ be the temperature of the junction (say B). Thermal resistance of all the three rods is equal. Rate of heat flow through AB + Rate of heat flow through CB = Rate of heat flow through BD
$\therefore \frac{90^{\circ }-\theta }{R}+\frac{90^{\circ }-\theta }{R}=\frac{\theta -0}{R}$
Here, R = Thermal resistance
$\therefore 3\theta =180^{\circ }or\theta =60^{\circ }$
NOTE
Rate of heat flow
$(H)=\frac{Temperaturedifference(TD)}{Thermalresistance(R}$
where, $R=\frac{l}{KA}$
K = Thermal conductivity of the rod.
This is similar to the current flow through a resistance (R) where current (i) = Rate of flow of charge
$\frac{Potentialdifference(PD)}{Electricalresistance(R)}$
Here, R $=\frac{1}{\sigma A}$ where $\sigma$ = Electrical conductivity